Robust adaptive synchronization of uncertain dynamical networks

This Letter studies local and global robust adaptive synchronizations in uncertain dynamical networks. For complex dynamical networks with unknown but bounded nonlinear couplings, with known or unknown bounds, some robust adaptive controllers are designed in this Letter, which can ensure that the state of a dynamical network locally or globally asymptotically synchronize with an arbitrarily assigned state of an isolate node of the network. The Letter also investigates the synchronization problem where the dynamics of the coupled states are different from that of the uncoupled states. The key idea is to suitably combine the Lyapunov stability theory with a good update law for estimating the unknown network coupling parameters in the design of the controllers. Two examples are simulated, using the smooth chaotic Chen system and the piecewise-continuous chaotic Chua circuit, respectively, as the nodes of the dynamical network, which demonstrate the effectiveness of the proposed controllers design methods.